Receiver used in marker localization sensing system using coherent detection

ABSTRACT

A receiver for determining the location of a marker that is excited with an exciting waveform. A sensing array having coils is used to sense magnetic flux from the resonating marker. The coils provide inputs to the receiver. The receiver includes a correlation processor for analyzing the inputs in a coherent manner. The receiver determines the phase component of each of the inputs and compensates for differences.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No.10/334,700 filed Dec. 30, 2002, U.S. patent application Ser. No.10/382,123, filed Mar. 4, 2003, and U.S. patent application Ser. No.10/679,801 filed Oct. 6, 2003 all of which are incorporated herein byreference in their entirety.

BACKGROUND

Implantable markers have been used to identify locations within objects,such as a human body. For example, a marker may be implanted in apatient within an organ of interest. As the patient moves, the markercan be used to track the location of the organ. Various techniques havebeen used to identify the location of such markers.

As described in my co-pending U.S. patent applications noted above, onetechnique for locating a marker is by measuring the magnetic fluxgenerated by the marker upon excitation from a source. The measurementof the magnetic flux is typically performed by an array of sensingelements that together form a sensing array. In some sensing arrays,each of the sensing elements has their output coupled to their owndedicated amplifier circuit.

The signals from the sensing elements are then output to a receiver thatis operative to extract the signal portion from the sensing elementsfrom noise, which may be caused from various sources including theexcitation from the source, co-channel or cross-channel interferencebetween sensing elements, radiation sources in the examinationenvironment, etc . . .

The design of a receiver suitable for use with magnetic flux sensingsystems has been problematic and challenging.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of an example of a system for estimatingthe location of wireless implantable markers.

FIG. 2 is a block diagram illustrating components of the system of FIG.1 including a sensing subsystem.

FIG. 3A is an exploded isometric view showing individual components of asensing subsystem in accordance with an embodiment of the invention.

FIG. 3B is a top plan view of an example of a sensing assembly of asensing subsystem.

FIG. 4 is a schematic diagram of a suitable preamplifier for use withthe sensing subsystem of FIG. 3.

FIG. 5 is a schematic diagram of a receiver formed in accordance withthe present invention.

FIG. 6 is a graphical illustration of an excitation pulse and a ringingresponse signal.

FIG. 7 is a flow diagram illustrating the process of the presentinvention.

FIG. 8 is a flow diagram illustrating the process of determining aresonant frequency of a marker.

FIG. 9 is a block diagram of a portion of the processing of one channelof the receiver.

FIG. 10 is a block diagram in the frequency domain of a model for thecoupling between the excitation pulse and the response signal.

FIG. 11 is a block diagram in the time domain of a model for thecoupling between the excitation pulse and the response signal where thedirect path is ignored.

FIG. 12 is an example of a response signal from a marker when theexcitation pulse is at resonance to the marker resonance.

FIG. 13 is an example of a response signal from a marker when theexcitation pulse is off resonance to the marker resonance.

FIG. 14 is a graph of the relative sensitivity of a coherent detectorfor various parameters.

FIG. 15 is a graph of efficiency for a constant energy case.

FIG. 16 is a graph of efficiency for a constant amplitude case.

FIG. 17 is a graph of efficiency for a saturated marker case.

FIG. 18 is a graph of efficiency using a thirty-two cycle rectangularwindow.

FIG. 19 is a graph of efficiency using a thirty-two cycle Hammingwindow.

FIG. 20 is a graph of efficiency using a thirty-two cycle Blackmanwindow.

Sizes of various depicted elements are not necessarily drawn to scale,and these various elements may be arbitrarily enlarged to improvelegibility. Also, the headings provided herein are for convenience onlyand do not necessarily affect the scope or meaning of the claimedinvention.

DETAILED DESCRIPTION

The present invention provides a receiver apparatus that receives andprocesses input signals from a magnetic flux sensing array. In oneembodiment, the sensing array includes multiple electromagnetic fieldsensors (also referred to as sensing elements) arranged in a locallyplanar array (e.g., an array in a common plane), and multiple sensesignal output paths coupled to the sensors. The sensors and thecorresponding output paths are configured to provide an output signalrepresenting at least a portion of an electromagnetic field emitted bythe marker; the output signal from a specific sensor is proportional tothe component of the field that is substantially perpendicular to theplane of the sensor integrated over its aperture. Again, although oneembodiment is described herein where the sensing array is substantiallyformed in a common plane, the methods and systems of the presentinvention may also be used with non-common plane sensing arrays.

The invention will now be described with respect to various embodiments.The following description provides specific details for a thoroughunderstanding of, and enabling description for, these embodiments of theinvention. However, one skilled in the art will understand that theinvention may be practiced without these details. In other instances,well-known structures and functions have not been shown or described indetail to avoid unnecessarily obscuring the description of theembodiments of the invention.

Description of Suitable Systems

FIG. 1 is a perspective view showing an example of a system 100 forenergizing and locating one or more wireless markers inthree-dimensional space. The system includes an excitation source andsensor array 102 supported by a movable arm 104. The arm 104 is securedto a base unit 106 that includes various components, such as a powersupply, computer (such as an industrial personal computer), and inputand output devices, such as a display 108. Many of these components aredescribed in detail below.

The system 100 may be used with guided radiation therapy to accuratelylocate and track a target in a body to which guided radiation therapy isdelivered. Further details on use of the system with such therapy may befound in U.S. patent application Ser. No. 09/877,498, entitled “GuidedRadiation Therapy System,” filed Jun. 8, 2001, which is hereinincorporated by reference. In general, a radiation source providesradiation for irradiating a tumor or other area of a patient or subject.Because of the toxic nature of the radiation, it is important toprecisely and accurately focus the radiation onto the desired site. Inaccordance with the present invention, the system is operative to locatea marker implanted or attached (generically “associated”) in or near thetumor, the marker acting as a guide point for the radiation therapy. Inaccordance with one aspect of the present invention, the system 100 issynchronized with the radiation source such that potentially interferingeffects from the radiation source is not being applied during thelocating process. In one embodiment, the locating process is interleavedin time with the potentially interfering operations of the radiationsource (typically a linear accelerator).

FIG. 2 is a block diagram of certain components of the system 100. Inparticular, the excitation source and sensor array 102 includes anexcitation system 202 and a sensing subsystem 204. The excitation system202 outputs electromagnetic energy to excite at least one wirelessmarker 206, and the sensing system 204 receives electromagnetic energyfrom the marker. Details regarding the sensing subsystem 204 areprovided below.

A signal processing subsystem 208 provides signals to the excitationsubsystem 202 to generate the excitation signals. In the embodimentdepicted herein, excitation signals in the range of 300 to 500 kilohertzmay be used. The signal processing subsystem 208 also receives signalsfrom the sensing subsystem 204. The signal processing subsystem 208filters, amplifies and correlates the signals received from the sensingsubsystem 204 for use in a computer 210.

The computer 210 may be any suitable computer, such as an industrialpersonal computer suitable for medical applications or environments. Oneor more input devices 212 are coupled to the computer and receive userinput. Examples of such input devices 212 include keyboards,microphones, mice/track balls, joy sticks, etc. The computer generatesoutput signals provided to output devices 214. Examples of such outputdevices include the display device 108, as well as speakers, printers,and network interfaces or subsystems to connect the computer with othersystems or devices.

Unless described otherwise herein, several aspects of the invention maybe practiced with conventional systems. Thus, the construction andoperation of certain blocks shown in FIG. 2 may be of conventionaldesign, and such blocks need not be described in further detail to makeand use the invention because they will be understood by those skilledin the relevant art.

Description of Suitable Sensing Subsystems

FIG. 3A is an exploded isometric view showing several components of thesensing subsystem 204. The subsystem 204 includes a sensing assembly 301having a plurality of coils 302 formed on or carried by a panel 304. Thecoils are arranged in a sensor array 305. The panel 304 may be asubstantially non-conductive sheet, such as KAPTON® produced by DuPont.KAPTON® is particularly useful when an extremely stable, tough, and thinfilm is required (such as to avoid radiation beam contamination), butthe panel 304 may be made from other materials. For example, FR4(epoxy-glass substrates), GETEK and Teflon-based substrates, and othercommercially available materials can be used for the panel 304.Additionally, although the panel 304 may be a flat, highly planarstructure, in other embodiments, the panel may be curved along at leastone axis. In either embodiment, the panel is at least substantiallylocally planar such that the plane of one coil is at least substantiallycoplanar with the planes of adjacent coils. For example, the anglebetween the plane defined by one coil relative to the planes defined byadjacent coils can be from approximately 0° to 10°, and more generallyis less than 5°. In some circumstances, however, one or more of thecoils may be at an angle greater than 10° relative to other coils in thearray.

The sensing subsystem 204 shown in FIG. 3A can further include alow-density foam spacer or core 320 laminated to the panel 304. The foamcore 320 can be a closed-cell Rohacell foam. The foam core 320 ispreferably a stable layer that has a low coefficient of thermalexpansion so that the shape of the sensing subsystem 204 and therelative orientation between the coils 302 remains within a definedrange over an operating temperature range.

The sensing subsystem 204 can further include a first exterior cover 330a on one side of the sensing subsystem and a second exterior cover 330 bon an opposing side. The first and second exterior covers 330 a-b can bethin, thermally stable layers, such as Kevlar or Thermount films. Eachof the first and second exterior covers 330 a-b can include electricshielding 332 to block undesirable external electric fields fromreaching the coils 302. The electric shielding is configured to preventor minimize the presence of eddy currents caused by the coils 302. Theelectric shielding can be a plurality of parallel legs of gold-plated,copper strips to define a comb-shaped shield in a configuration commonlycalled a Faraday shield. It will be appreciated that the shielding canbe-formed from other materials that are suitable for shielding. Theelectric shielding can be formed on the first and second exterior coversusing printed circuit board manufacturing technology or othertechniques.

The panel 304 with the coils 302 is laminated to the foam core 320 usingan epoxy or another type of adhesive. The first and second exteriorcovers 330 a-b are similarly laminated to the assembly of the panel 304and the foam core 320. The laminated assembly forms a rigid, lightweightstructure that fixedly retains the arrangement of the coils 302 in adefined configuration over a large operating temperature range. As such,the sensing subsystem 204 does not substantially deflect across itssurface during operation. The sensing subsystem 204, for example, canretain the array of coils 302 in the fixed position with a deflection ofno greater than ±0.5 mm, and in some cases no more than ±0.3 mm. Thestiffness of the sensing subsystem 204 provides very accurate andrepeatable monitoring of the precise location of leadless markers inreal time.

The sensing subsystem 204 can also have a low mass per unit area in theplane of the sensor coils 302. The “mass-density” is defined by the massin a square centimeter column through the thickness of the sensingsubsystem 204 orthogonal to the panel 304. In several embodiments, thesensing subsystem 204 has a low-density in the region of the coils 302to allow at least a portion of the sensing subsystem 204 to dwell in aradiation beam of a linear accelerator used for radiation oncology. Forexample, the portion of the sensing subsystem 204 including the coils302 can have a mass density in the range of approximately 1.0 gram/cm²or less. In general, the portion of the sensing subsystem that is toreside in the beam of a linear accelerator has a mass-density betweenapproximately 0.1 grams/cm² and 0.5 grams/cm², and often with an averagemass-density of approximately 0.3 grams/cm². The sensing subsystem 204can accordingly reside in a radiation beam of a linear acceleratorwithout unduly attenuating or contaminating the beam. In one embodiment,the sensing subsystem 204 is configured to attenuate a radiation beam byapproximately only 0.5% or less, and/or increase the skin dose in apatient by approximately 80%. In other embodiments, the panel assemblycan increase the skin dose by approximately 50%. Several embodiments ofthe sensing subsystem 204 can accordingly dwell in a radiation beam of alinear accelerator without unduly affecting the patient or producinglarge artifacts in x-ray films.

In still another embodiment, the sensing subsystem 204 can furtherinclude a plurality of source coils that are a component of theexcitation subsystem 202. One suitable array combining the sensingsubsystem 204 with source coils is disclosed in U.S. patent applicationSer. No. 10/334,700, entitled PANEL-TYPE SENSOR/SOURCE ARRAY ASSEMBLY,filed on Dec. 30, 2002, which is herein incorporated by reference.

FIG. 3B further illustrates an embodiment of the sensing assembly 301.In this embodiment, the sensing assembly 301 includes 32 sense coils302; each coil 302 is associated with a separate channel 306 (shownindividually as channels “Ch 0 through Ch 31 ”). The overall dimensionof the panel 304 can be approximately 40 cm by 54 cm, but the array 305has a first dimension D₁ of approximately 40 cm and a second dimensionD₂ of approximately 40 cm. The coil array 305 can have other sizes orother configurations (e.g., circular) in alternative embodiments.Additionally, the coil array 305 can have more or fewer coils, such as8-64 coils; the number of coils may moreover be a power of 2.

The coils 302 may be conductive traces or depositions of copper oranother suitably conductive metal formed on the KAPTON® sheet. Each coil302 has traces with a width of approximately 0.15 mm and a spacingbetween adjacent turns within each coil of approximately 0.15 mm. Thecoils 302 can have approximately 15 to 90 turns, and in specificapplications each coil has approximately 40 turns. Coils with less than15 turns may not be sensitive enough for some applications, and coilswith more than 90 turns may lead to excessive voltage from the sourcesignal during excitation and excessive settling times resulting from thecoil's lower self-resonant frequency. In other applications, however,the coils 302 can have less than 15 turns or more than 90 turns.

As shown in FIG. 3B, the coils 302 are arranged as square spirals,although other configurations may be employed, such as arrays ofcircles, interlocking hexagons, triangles, etc. Such square spiralsutilize a large percentage of the surface area to improve the signal tonoise ratio. Square coils also simplify design layout and modeling ofthe array compared to circular coils; for example, circular coils couldwaste surface area for linking magnetic flux from the wireless markers206. The coils 302 have an inner diameter of approximately 40 mm, and anouter diameter of approximately 62 mm, although other dimensions arepossible depending upon applications. Sensitivity may be improved withan inner diameter as close to an outer diameter as possible givenmanufacturing tolerances. In several embodiments, the coils 32 areidentical to each other or at least configured substantially similarly.

The pitch of the coils 302 in the coil array 305 is a function of, atleast in part, the minimum distance between the marker and the coilarray. In one embodiment, the coils are arranged at a pitch ofapproximately 67 mm. This specific arrangement is particularly suitablewhen the wireless markers 206 are positioned approximately 7-27 cm fromthe sensing subsystem 204. If the wireless markers are closer than 7 cm,then the sensing subsystem may include sense coils arranged at a smallerpitch. In general, a smaller pitch is desirable when wireless markersare to be sensed at a relatively short distance from the array of coils.The pitch of the coils 302, for example, is approximately 50%-200% ofthe minimum distance between the marker and the array.

In general, the size and configuration of the coil array 305 and thecoils 302 in the array 305 depend on the frequency range in which theyare to operate, the distance from the wireless markers 206 to the array,the signal strength of the markers, and several other factors. Thoseskilled in the relevant art will readily recognize that other dimensionsand configurations may be employed depending, at least in part, on adesired frequency range and distance from the markers to the coils.

The coil array 305 is sized to provide a large aperture to measure themagnetic field emitted by the markers. It can be particularlychallenging to accurately measure the signal emitted by an implantablemarker that wirelessly transmits a marker signal in response to awirelessly transmitted energy source because the marker signal is muchsmaller than the source signal and other magnetic fields in a room(e.g., magnetic fields from CRTs, etc.). The size of the coil array 305can be selected to preferentially measure the near field of the markerwhile mitigating interference from far field sources. In one embodiment,the coil array 305 is sized to have a maximum dimension D₁ or D₂ acrossthe surface of the area occupied by the coils that is approximately 100%to 300% of a predetermined maximum sensing distance that the markers areto be spaced from the plane of the coils. Thus, the size of the coilarray 305 is determined by identifying the distance that the marker isto be spaced apart from the array to accurately measure the markersignal, and then arrange the coils so that the maximum dimension of thearray is approximately 100%-300% of that distance. The maximum dimensionof the coil array 305, for example, can be approximately 200% of thesensing distance at which a marker is to be placed from the array 305.In one specific embodiment, the marker 206 has a sensing distance of 20cm and the maximum dimension of the array of coils 302 is between 20 cmand 60 cm, and more specifically 40 cm.

A coil array with a maximum dimension as set forth above is particularlyuseful because it inherently provides a filter that mitigatesinterference from far field sources. It will be appreciated that in sucha configuration the signal strength from the wireless marker decreasesproportionally to the square of the distance. However, far field signalsfrom electromagnetic noise generated by other systems in the environmentdecrease proportionally to the cube of the distance. Thus, if thewireless marker 206 is positioned approximately 20 cm from the sensingsubsystem 204, and a diameter or maximum dimension of the sensingsubsystem is approximately 40 cm, signals from the wireless marker dropoff at a square of the distance from the sensing subsystem whileenvironmental noise drops off at a cube of the distance. Theenvironmental noise is thus filtered by the sensing subassembly 204 toprovide better signals to the signal processing subsystem 208.

The size or extent of the array may be limited by several factors. Forexample, the size of the sensing assembly 301 should not be so large asto mechanically interfere with the movable arm 104 (FIG. 1), the baseunit 106 (FIG. 1), or other components, such as a patient couch,rotating gantry of a radiation therapy machine, etc. (not shown in FIG.1). Also, the size of the array may be limited by manufacturingconsiderations, such as a size of available panels 304. Further, makinga dimension or width of the coil array 305 larger than twice thedistance to the wireless marker 206 may yield little performanceimprovement, but increase manufacturing costs and increase sensitivityto interference.

The coils 302 are electromagnetic field sensors that receive magneticflux produced by the wireless marker 206 and in turn produce a currentsignal representing or proportional to an amount or magnitude of acomponent of the magnetic field through an inner portion or area of eachcoil. The field component is also perpendicular to the plane of eachcoil 302. Importantly, each coil represents a separate channel, and thuseach coil outputs signals to one of 32 output ports 306. A preamplifier,described below, may be provided at each output port 306. Placingpreamplifiers (or impedance buffers) close to the coils minimizescapacitive loading on the coils, as described herein. Although notshown, the sensing assembly 301 also includes conductive traces orconductive paths routing signals from each coil 302 to its correspondingoutput port 306 to thereby define a separate channel. The ports in turnare coupled to a connector 308 formed on the panel 304 to which anappropriately configured plug and associated cable may be attached.

The sensing assembly 301 may also include an onboard memory or othercircuitry, such as shown by electrically erasable programmable read-onlymemory (EEPROM) 310. The EEPROM 310 may store manufacturing informationsuch as a serial number, revision number, date of manufacture, and thelike. The EEPROM 310 may also store per-channel calibration data, aswell as a record of run-time. The run-time will give an indication ofthe total radiation dose to which the array has been exposed, which canalert the system when a replacement sensing subsystem is required.

While shown in only one plane, additional coils or electromagnetic fieldsensors may be arranged perpendicular to the panel 304 to help determinea three-dimensional location of the wireless markers 206. Adding coilsor sensors in other dimensions could increase total energy received fromthe wireless markers 206 by 3 dB. However, the complexity of such anarray may increase three-fold or more. The inventors have found thatthree-dimensional coordinates of the wireless markers 206 may be foundusing the planar array shown in FIG. 3B.

Description of a Suitable Preamplifier

Implementing the sensing subsystem 204 may involve severalconsiderations. First, the coils 302 may not be presented with an idealopen circuit. Instead, they may well be loaded by parasitic capacitancedue largely to traces or conductive paths connecting the coils to thepreamplifiers, as well as a damping network (described below) and aninput impedance of the preamplifiers (although a low input impedance ispreferred). These combined loads result in current flow when the coils302 link with a changing magnetic flux. Any one sense coil 302, then,links magnetic flux not only from the wireless marker 206, but also fromall the other sense coils as well. These current flows should beaccounted for in downstream signal processing.

A second consideration is the capacitive loading on the coils 302. Ingeneral, it is desirable to minimize the capacitive loading on the coils302. Capacitive loading forms a resonant circuit with the coilsthemselves, which leads to excessive voltage overshoot when theexcitation subsystem 202 is energized. Such a voltage overshoot shouldbe limited or attenuated with a damping or “snubbing” network across thecoils 302. A greater capacitive loading requires a lower impedancedamping network, which can result in substantial power dissipation andheating in the damping network.

Another consideration is to employ preamplifiers that are low noise. Thepreamplification can also be radiation tolerant because one applicationfor the sensing subsystem 204 is with radiation therapy systems that uselinear accelerators (LINAC). As a result, PNP bipolar transistors anddiscrete elements may be preferred. Further, a DC coupled circuit may bepreferred if good settling times cannot be achieved with an AC circuitor output, particularly if analog to digital converters are unable tohandle wide swings in an AC output signal.

FIG. 4, for example, illustrates an embodiment of a snubbing network 402having a differential amplifier 404. The snubbing network 402 includestwo pairs of series coupled resistors and a capacitor bridgingtherebetween. A biasing circuit 406 allows for adjustment of thedifferential amplifier, while a calibration input 408 allows both inputlegs of the differential amplifier to be balanced. The sensor coil 302is coupled to an input of the differential amplifier 404, followed by apair of high voltage protection diodes 410. DC offset may be adjusted bya pair of resistors coupled to bases of the input transistors for thedifferential amplifier 404 (shown as having a zero value). Additionalprotection circuitry is provided, such as ESD protection diodes 412 atthe output, as well as filtering capacitors (shown as having a 10 nFvalue).

The Receiver

The signal processing subsystem 208 shown in FIG. 2 is also referred toherein as a receiver. The receiver 208 is operative to receive thesignals from the sensing subsystem 204 and perform various signalprocessing. As set forth below, several of these signal processingtechniques and associated structures significantly enhance theperformance of the system 100.

Referring to FIG. 5, the sense coils 32 each provide a signal to arespective amplifier 404. The amplifier then provides the amplifiedsignal to an associated analog-to-digital (AID) converter 502 thatconverts the analog amplified signal into a digital representation, suchas an 8-bit, 16-bit or 32-bit digital signal, depending upon designconsiderations. In one embodiment, an out-of band dither is added tolinearize the AID converters 502. Note that the AID converters 502 areall clocked with a common clock signal to assure uniformity. Further,because the excitation 601 and response 603 waveforms are in the 300-500KHz range, the A/D 502 would have to sample at a much higher frequency.In one embodiment, the A/D 502 samples at 16 MHz.

Thus, the receiver 208 receives a plurality of digital inputs from theA/D converters 502. As will be seen below, the receiver 208 will act onthe plurality of digital inputs to substantially eliminate noise,interference, and other “non-signal” effects to provide a highsignal-to-noise ratio (SNR) plurality of digital outputs. These digitaloutputs can then be used to locate the marker using various locatingtechniques, such as the ones described in co-pending U.S. patentapplication Ser. No. 10/679,801 filed Oct. 6, 2003 entitled “Method andSystem for Marker Localization” and previously incorporated byreference.

As noted above, the excitation source 202 emits, in one example, atriangular pulse of exciting energy at a frequency of about 300 to 500kilohertz. FIG. 6 shows one example of such an exciting pulse 601 thatis emitted from the excitation source 202. The exciting pulse 601 has aduration of (T₁-T₀). In one embodiment, the duration of the pulse 601 is16 cycles, or for a signal at 400 KHz, about 40 microseconds. It can beappreciated that shorter or longer excitation pulses 601 may be useddepending upon various design parameters.

Note that while a triangular shaped pulse is used for the excitation inone embodiment, other shaped pulses, such as sinusoidal, sawtooth, orsquare wave excitation may be used. However, a triangular waveform willadvantageously excite a marker that exhibits high inductive qualities.Further, because of the relatively high amplitude of the exciting pulse601, in some circumstances, the coils 302 of the sensing array 204 maybe saturated. Further, when the exciting pulse 601 is being emitted,this would ordinarily be a source of significant noise to the coils 302.Because of this, the operation of the system 100 utilizes a timemultiplexed methodology where there is an excitation interval (T₁-T₀)and a observation interval (T₂-T₁).

Thus, after the excitation interval at time T₁, the excitation source202 stops emission and the sensing array 204 “listens” during theobservation interval for the decaying ringing response 603 of the markerthat has been excited. The ringing response 603 will typically be adamped sinusoidal signal. This observation interval is from time T₁ totime T₂. In one embodiment, the duration of the listening time is 32cycles, or for a signal at 400 KHz, about 80 microseconds. Thecombination of one excitation interval and its following observationinterval is referred, to herein also as an excitation and observationsubinterval.

As will be seen below, in one aspect of the present invention, theexcitation interval or observation interval can be adjusted to match thecharacteristics of the marker. Thus, the length of excitation intervalor observation interval is programmable (or automated) in the receiver208 in order to optimize the sensing system 100. Note that FIG. 6 is notdrawn to scale and is merely illustrative.

Because of the relatively short time frames needed to perform theexcitation and listening operations (on the order of 120 microseconds),thousands of iterations of the excitation and listening operations canbe performed in a single second. In. principle, the response signals 603should be very similar to each other over various cycles of excitationand listening. Thus, in one embodiment, the ringing response signals 603that are sensed by the coils 302 of the sensing array 204 can be mergedover several hundred (or even thousands) excitation and listening cyclesto improve the signal-to-noise ratio. In one embodiment, responsesignals 603 over 100 milliseconds are averaged. This corresponds toroughly 1000 excitation and listening cycles.

The above process can be seen in FIG. 7, which is a flow diagram of theoverall process of one aspect of the present invention. In particular,at box 701, the excitation source 202 emits an exciting pulse 601 duringan excitation interval. At box 703, during a observation interval, thesense coils 302 sense the magnetic flux from the marker and provide dataas inputs to the receiver 208. This process is repeated for N iterationsat box 705 and at box 707, the signals input to the receiver 208 areaveraged. Then, further processing is performed on the averaged inputs(see below).

Additionally shown in FIG. 7 are other aspects of the present inventionthat may be optionally included. These include the implementation of atiming dither at box 711, synchronization to a radiation source toeliminate interference at box 713, and tuning the system 100 to themarkers at box 709. All of these aspects are discussed below.

Correlation Receiver

In one embodiment, a correlation receiver is provided. As detailedbelow, it has been found that coherent receiver design is required toretain the relative polarity of each channel; it will also provide a 3dB signal-to-noise performance improvement over an incoherent receiver.

The response signals 603 that are received by the coils 302 and inputinto the receiver have an unknown phase. Thus, the plurality of inputsare complex signals that each have an in-phase component and aquadrature component. The coherent receiver 208 operates by extractingthese components of the inputs.

The phase shift occurs because the marker oftentimes does not have aresonant frequency that is precisely matched to the exciting pulse 601.This is due to manufacturing tolerances and other factors. Because ofthe mismatch between the resonant frequency of the marker and theexciting pulse 601, there will be a phase component of the signal sensedby the coils 302. Further, in the presence of a strong magnetic signal,the markers may enter saturation in which case there is a phase shiftdue to losses in the marker.

However, it has been found that the phase shift is substantially thesame for all channels (i.e. each coil). As will be seen below, thereceiver analyzes the signals from all of the channels and determinesthe most likely phase shift. Once the phase shift has been determined,this phase shift is corrected from the signals (such as by removal) andthe real portion of the signal can be extracted. By performing theestimation and removal of the phase shift, this is substantiallyequivalent to coherent detection of the input signals. In oneembodiment, the coherent detection is implemented by a digital signalprocessor 504. However, in alternative embodiments, the processing oranalysis can be done using programmable logic devices or even softwarerunning on a general purpose microprocessor.

Receiver Tunable to Resonator Frequency and Ring Time

As noted above at box 709 of FIG. 7, in another aspect of the presentinvention, the receiver 208 is adaptable to work in coordination withthe excitation source to tune the system 100 to the specificcharacteristics of the marker. Specifically, the excitation source 202has an adjustable frequency that can be tuned in accordance withanalysis made by the receiver 208.

Because of various manufacturing variances and other factors, the markermay not have an accurately predictable resonant frequency. Thus, thereceiver 208 identifies the resonant frequency of the marker andprovides that information to the excitation source 202. The excitationsource 202 can then provide an exciting pulse 601 at a frequency that isclosely matched to the resonant frequency of the marker. In this manner,better performance can be obtained by the system 100.

In one embodiment, the determination of the resonant frequency of themarker is done in an iterative manner. The process of detailed in FIG.8, where at box 801, the excitation source 202 emits an exciting pulse601 at a starting frequency F_(s). In one embodiment, the startingfrequency is the lower range of possible resonant frequencies for themarker. Depending upon manufacturing tolerances, the marker may have awide marker resonant frequency range, for example, between 300-500 KHz.In this example, F_(s) would then be 300 KHz.

Next, at box 803, data from the sense coils 302 is gathered by thereceiver 208 and stored. At box 805, the frequency of the last emittedexciting pulse 601 is incremented by an amount ΔF. The value of ΔF isvariable and depends upon the amount of resonant frequency accuracydesired for the system 100. However, in one embodiment, ΔF is 2 KHz. Theprocess is repeated until an ending frequency F_(e) has been reached,for example 500 KHz. The frequencies of the exciting pulses ranging fromF_(s) to F_(e) incremented by ΔF constitute a set of frequencies used toexcite the marker. This set of frequencies may be large or smalldepending upon the ΔF, F_(s) and F_(e).

In alternative embodiment, the spacing ΔF is chosen as a fixedpercentage bandwidth which has advantages in accuracy and/or processingtime in certain applications particularly when the marker Q (rather thanbandwidth) tends to be constant over a large frequency range. One suchapproach would use a step size approximating the half power points ofthe marker frequency response. An example would be 1.5% steps resultingin a set consisting of: 300.00, 304.50, 309.07, . . . , 497.70, 505.16kHz. It is understood that depending on the marker characteristics,other sets of excitation frequency may be used and the invention acceptsan arbitrary arrangement of excitation frequencies.

Next, at box 809, the data received for these iterations is analyzed andthe frequency for the emitting pulse 601 that provided the strongest (orotherwise best) signal is chosen as the resonant frequency of the markerat box 811. The data may also be referred to as a resonance set ofplurality of inputs from the sense coils 302. It can be appreciated thatvarious methods for determining the resonant frequency may be possibleand that only one implementation is given herein. The process above maybe implemented, for example, in a resonant frequency and ring timecontrol processor 510.

An alternative method of determining the resonant frequency wouldinterpolate the resultant response. This is particularly beneficial ifthe set of frequencies can guarantee multiple samples within a markerfrequency response bandwidth. It is understood that this interpolationcan be conducted in a number of ways, two examples of which are: a)parabolic fitting to find an estimate of the peak signal value andresonant frequency using neighboring data points to the one thatrepresents the highest energy response; or, b) least squares errorfitting to a multi-parameter model of the marker frequency response.

In yet another alternative embodiment to the process of FIG. 8, thefrequency range may be searched with a sparse set of excitationfrequencies. Then, the excitation is iterated with a higher resolutionset of frequencies in the neighborhood surrounding the candidateresonant frequency. Multiple iterations may be used in combination withinterpolation.

In other words, a first set of frequencies that are relatively sparselyspaced is used to excite the marker. Based upon the information receivedby the receiver 208, the marker resonant frequency can be narrowed down.A second set of frequencies that is more densely populated around thefrequency band of interest (as ascertained by the first set offrequencies) is then used to excite the marker. This process can berepeated until the desired resolution of the marker resonant frequencyhas been obtained.

Yet another embodiment of the process of FIG. 8 would use wide-bandwidthexcitation signals rather than sinusoidal signals that could excitemultiple markers at once and then process the data, for example, usingspectral estimation techniques, to determine the resonant frequencies ofthe markers. An example of such a signal would be a high energy pulse,shaped to concentrate its energy in the frequency band of interest. Inaddition, the signal could be repeated multiple times and averagingemployed to improve the sensitivity of the resonant frequencyestimation.

Subsequent excitation is performed at the marker resonant frequency.Further, the receiver 208 is adjusted to correlate using the markerresonant frequency. This type of initial “calibration” by identifyingthe appropriate excitation frequency has been found to provideadvantageous results.

Additionally, the receiver 208 may be is adapted to the ring time of themarker. Various marker designs may have varying ring times. For example,some markers made from certain materials may have ring times thatextinguish quite rapidly compared to other markers made of differingmaterial. Because of this, it may be advantageous to adjust theexcitation pulse interval and the observation interval.

In the example given above, an excitation pulse of 16 cycles and alistening time of 32 cycles is used. However, these parameters may needto be changed depending upon operating conditions and marker variations.Therefore, in accordance with the present invention, the receiver 208has control circuitry that can control the operation of the excitationsource 202 not only in the frequency domain, but also the time domainfor the exciting pulse 601. The receiver 208 includes the resonantfrequency and ring time control processor 510 that can modify the lengthof the observation interval. These parameters may be controlledaccording to preprogrammed instructions or manually by the operator ofthe system 100 through a user interface.

In accordance with another aspect of the present invention, the receiver208 also includes signal processing that uses a weighting of the dataobtained during the observation interval. This is also referred to asapplying a “window” filter to the observation interval. In oneembodiment, the window is a Blackman window. The effect of the Blackmanwindowing is to improve the frequency selectivity of the receiver byreducing the effects of other markers tuned to different frequencies.

In another embodiment the window filter is a “matched filter” that has awindow that emulates the decay signature of the marker resonance. Theeffect of the matched filter windowing is to improve the sensitivity ofthe receiver.

In some applications, more than one marker is within the field ofinterest. Typically, three different markers having varying resonantfrequencies are used. Because of this, all three markers may have aresponse to the exciting pulse 601 at the resonant frequency of one ofthe markers. The signals from the two other markers may add noise to thedesired signal to be detected by the receiver. Because of this, as willbe seen below, various windows can be applied to reduce the sensitivityof the receiver to other markers in the field of interest. Still, onedrawback of the window filtering is decreased sensitivity to the markerof interest.

The spectral data can be simultaneously used to improve detectionrobustness of real markers versus noise spikes. In one embodiment of thesystem, the data is checked for consistency with the marker frequencyresponse model. The system can reject candidates if the estimatedbandwidth does not conform to the design parameters of the markers, forexample, having a bandwidth outside of the acceptable manufacturingtolerance range. Additional model characteristics that may bedistinguished include acceptable energy levels and acceptableseparations of markers in the frequency domain. The system can alsoreject signals that are not coherent with the excitation signal phase ascharacterized by independent sources of noise in the environment.

Synchronization with Radiation Beam

In one application of the present invention, the system 100 is used inproximity to a radiation source (such as a linear accelerator or aparticle beam accelerator) that is used for the treatment of a human,such as during radiation therapy of a cancer patient. In such aninstance, the system 100, and particularly, the receiver 208, themarkers, or the sensing coils may be adversely interfered with by theoperation of radiation source (not only the emitted radiation, but thecircuitry of the radiation source itself). Therefore, the system 100 isadapted to operate when the radiation source is off. This can becoordinated, for example, by the use of a radiation control signal 506(see FIG. 5) between the radiation source and the receiver 208 and/orsystem 100. When the radiation source is active, the control signaltravels to the receiver 208 and/or system 100 in order to put the system100 into a “standby” mode. The radiation control signal may be a simplebinary signal.

As one example, radiation may be delivered by the radiation source in a150 microsecond burst, occurring once every 10 milliseconds. In theexample given previously, one excitation and listening cycle may takeapproximately 120 microseconds. Therefore, in one embodiment, after aradiation burst (when the system 100 is in standby mode), perhaps on theorder of 80 excitation and listening cycles may be performed by thesystem 100 until the next radiation burst. This aspect of the presentinvention helps to negate the effect of any interference from theradiation source.

It is perhaps easiest to implement a control signal line between theradiation source and the system 100 to indicate when the radiation burstis occurring. However, this may not be commercially possible since themanufacturers of the radiation equipment and the vendors of the markerlocation equipment may not be able to coordinate these interface issues.

Therefore, in an alternative embodiment, the receiver 208 includes amatched filter or other device (designated as radiation detector 512)that can detect the presence of interference due to the operation of theradiation delivery apparatus, or any other interfering device thatoperates in a pulsed mode. If such interference is detected, then thereceiver 208 is operative to discard received input signals from thecoils 302 that occurred in that timeframe.

Receiver and Exciting Source Configured for Pseudo-random Excitation

The primary function of the receiver 208 is to suppress noise andinterference, while extracting signal from the received inputs. As notedabove, one of the techniques used for suppressing noise is to performaveraging over several observation intervals. However, it has been foundthat if the source of noise is periodic with a periodicity matched tothat of the excitation and observation interval, then the noise not onlywill not be removed by averaging, but may indeed masquerade as signal.

Several sources of noise and interference that may have the periodicityinclude computer equipment, cathode ray tube monitors, medicalequipment, and other electronics. In order to suppress this type ofperiodic noise, in another aspect of the present invention, theinitiation of each excitation pulse 601 is changed so as to not have aperiodic repetition.

In accordance with the present invention, the receiver 208 includes apseudo-random excitation dithering circuit 508 (see FIG. 5) that willrandomly offset the start timing of each exciting pulse 601 relative toprevious or future exciting pulses. In one embodiment, the ditheringcircuit 508 will offset the timing of each exciting pulse 601 by arandom fraction of one period of the carrier frequency of the excitingpulse 601, e.g., at 400 KHz dither from 0 to 2.5 microseconds. Theeffect of the dithering would spread out or “decohere” any periodicnoise, turning the periodic noise into random noise that can be reducedby signal processing.

Another method of achieving a similar result is the randomly vary thepolarity of each exciting pulse 601. For example a first exciting pulsemay start with a positive going cycle, while a second exciting pulse maystart with a negative going cycle. In other words, the first excitingpulse may be 180 degrees out of phase with the second exciting pulse.This random polarity of the exciting pulses 601 will also decohere anyperiodic noise, turning the periodic noise into random noise that can beeliminated by signal processing.

Yet another method of achieving a similar result is the randomly varythe starting phase of each exciting pulse 601. For example a firstexciting pulse may start with zero relative phase, while a secondexciting pulse may start at some random phase, while a third excitingpulse may start at another random phase. This random starting phase ofthe exciting pulses 601 will also decohere any periodic noise, turningthe periodic noise into random noise that can be eliminated by signalprocessing.

Frequency Orthogonality

In the foregoing embodiments described, the excitation intervals andobservation intervals are orthogonal temporally. In other words, theexcitation intervals are distinct from the observation intervals andthere is no overlap. In another embodiment, the receiver 208 may be usedwith a substantially continuous excitation pulse. In order to avoidinterference, the excitation pulse is at a first frequency that isdifferent from the returned frequency of the marker. This is referred toas frequency orthogonality. Because of this, the receiver 208 is adaptedto have a narrow bandpass filter to suppress the excitation frequencyand pass the returned frequency.

Mathematical and Signal Processing Foundation

As noted above, the receiver 208 uses coherent detection to increaseSNR. Assume that the marker signal sensed by each channel is applied toa complex correlation receiver, identical over all channels. It isfurther assumed that any unknown phase shift in the marker signal is, inthe absence of noise, common across all channels. If the actualphase—referred to as Φ—were known, coherent reception could be effectedby counter-rotating each estimate by this phase and discarding theimaginary parts. This is a linear operation, and the only discardedcomponent is the part of the noise that is orthogonal to the signal.

Any estimate of Φ from the data will be inexact. In a single channelcase, an estimate of Φ will be corrupted by noise. However, the presenceof multiple channels (i.e. multiple sense coils 302) permits a betterestimate of the necessary phase.

Ouasi-Coherent Detection Using Least-Mean Squares Estimate of theSignals

Consider multiple identical receiver channels in which the outputs ofthe integrators are sampled at the end of a common measurement interval,as in FIG. 9 depicting the n^(th) channel.

The output of each channel at the end of each measurement interval canbe modeled as in FIG. 9, where A_(n) is the signed scalar amplitude ofthe desired signal, Φ is an unknown phase shift common to all channels,and N_(n) is a complex zero-mean, uncorrelated error in the measurement.The data can be fit to the model in a least mean squares (LMS) sense asfollows.

Let the data of the n^(th) channel be represented as x_(n)+jy_(n). Thesum of the square magnitudes of the errors between the model and thedata is thus$E = {{\sum\limits_{n}{{{A_{n}{\mathbb{e}}^{j\phi}} - \left( {x_{n} + {j\quad y_{n}}} \right)}}^{2}}\quad = {{\sum\limits_{n}A_{n}^{2}} + \left( {x_{n}^{2} + y_{n}^{2}} \right) - {2{A_{n}\left\lbrack {{x_{n}\cos\quad\phi} + {y_{n}\sin\quad\phi}} \right\rbrack}}}}$

where the summation is taken over all channels. The model parametersA_(n) and Φ are chosen to minimize this quantity. Denoting the totalnumber of channels as N_(ch), the problem is one of determining N_(ch)+1parameters from 2N_(ch) data points.

The partials of the equation above with respect to the parameters are$\frac{\partial E}{\partial A_{n}} = {{2A_{n}} - {2\left\lbrack {{x_{n}\cos\quad\phi} + {y_{n}\sin\quad\phi}} \right\rbrack}}$$\frac{\partial^{2}E}{\partial A_{n}^{2}} = 2$$\frac{\partial E}{\partial\phi} = {\sum\limits_{n}{2{A_{n}\left\lbrack {{x_{n}\sin\quad\phi} - {y_{n}\cos\quad\phi}} \right\rbrack}}}$$\frac{\partial^{2}E}{\partial\phi^{2}} = {\sum\limits_{n}{2{A_{n}\left\lbrack {{x_{n}\cos\quad\phi} + {y_{n}\sin\quad\phi}} \right\rbrack}}}$

A solution that makes the first partials vanish, and keeps the secondpartials positive, is $\begin{matrix}{{{\hat{A}}_{n} = {{x_{n}\cos\quad\hat{\phi}} + {y_{n}\sin\quad\hat{\phi}}}}{\hat{\phi} = {\frac{1}{2}{Arg}\left\{ {\sum\limits_{n}\left( {x_{n} + {j\quad y_{n}}} \right)^{2}} \right\}}}} & {{Eq}.\quad 1}\end{matrix}$

Note that the hat notation is used to distinguish the estimates of theparameters from the actual values. The expression for Â_(n) is simplythe rule for counter-rotating each measurement through {circumflex over(Φ)} and taking the real part. The expression for {circumflex over (Φ)}is intuitively satisfying; it specifies that each complex data pointshould be squared (hence doubling its phase), and summed with allothers. The phase of the result is twice the phase of the estimate of Φ.Note, though, that halving the calculated phase yields two solutions,separated by ±π.

This results in a sign ambiguity in the estimate of A_(n). Thisambiguity is benign, as it applies to all channels in common for themeasurement interval used. If post-detection averaging (or an equivalentoperation) is intended, then this ambiguity will have to be resolved.When the SNR is high, this is easy to do by looking at the data.

Noise Performance of Quasi-Coherent Detection

It can be shown that, when the phase estimate is expressed in terms ofits error{circumflex over (Φ)}=Φ+ψthen the estimate of the signal in the k^(th) channel isÂ_(k) =A _(k)cosψ+ε_(k)cosψ+δ_(k)sinψ  Eq. 2where${2\psi} = {{Arg}\left\{ {\left\lbrack {{\sum\limits_{n}A_{n}^{2}} + {2A_{n}ɛ_{n}} + \left( {ɛ_{n}^{2} - \delta_{n}^{2}} \right)} \right\rbrack + {j\left\lbrack {{\sum\limits_{n}{2A_{n}\delta_{n}}} + {2ɛ_{n}\delta_{n}}} \right\rbrack}} \right\}}$

To keep the notation as simple as possible, the ambiguity in the sign ofthe estimate is suppressed in the following development, although itshould keep it in mind.

The noise components ε_(k) and δ_(k) are modeled as circular Gaussianrandom variables, with identical variances

e²

=E{ε_(k) ²}=E{δ_(k) ²}=E{N|²}/2.

To examine the performance of this detector in the presence of noise,the expected value and the second moment of Eq. 2 can be calculated.E{Â _(k) }=A _(k) E{cosψ}+E{ε _(k)cosψ}+E{δ _(k)sinψ}${{E\left\{ {\hat{A}}_{k}^{2} \right\}} = {\frac{A_{k}^{2}}{2} + {\frac{A_{k}^{2}}{2}{E\left\lbrack {\cos\quad 2\psi} \right\}}} + {\frac{1}{2}E\left\{ {ɛ_{k}^{2} + \delta_{k}^{2}} \right\}} + {\frac{1}{2}E\left\{ {\left( {ɛ_{k}^{2} - \delta_{k}^{2}} \right)\cos\quad 2\psi} \right\}} + {A_{k}E\left\{ {ɛ_{k}\cos\quad 2\psi} \right\}} + {A_{k}E\left\{ {\delta_{k}\sin\quad 2\psi} \right\}} + {E\left\{ {ɛ_{k}\delta_{k}\sin\quad 2\psi} \right\}}}}\quad$

Because ψ is a function of the noise components, the expectations arenot straightforward to calculate. It is shown below that, underconditions of high SNR, we may approximate $\begin{matrix}{{{E\left\{ {\hat{A}}_{k} \right\}} = {A_{k} + \frac{A_{k}\left\langle {\mathbb{e}}^{2} \right\rangle}{2{\sum\limits_{n}A_{n}^{2}}}}}{{E\left\{ {\hat{A}}_{k}^{2} \right\}} = {A_{k}^{2} + \frac{A_{k}^{2}\left\langle {\mathbb{e}}^{2} \right\rangle}{\sum\limits_{n}A_{n}^{2}} + \left\langle {\mathbb{e}}^{2} \right\rangle}}} & {{Eq}.\quad 3}\end{matrix}$

The signal-to-noise ratio of the k^(th) receiver channel, assuming idealcoherent detection, is A_(k) ²/E{ε_(k) ²}; the signal-to-noise acrossall channels is thus${SNR} = \frac{\sum\limits_{n}A_{k}^{2}}{N_{ch}\left\langle {\mathbb{e}}^{2} \right\rangle}$

In terms of the SNR, the moments calculated above are${E\left\{ {\hat{A}}_{k} \right\}} \cong {A_{k}\left\lbrack {1 + \frac{1}{2N_{ch}{SNR}}} \right\rbrack}$${E\left\{ {\hat{A}}_{k}^{2} \right\}} \cong {{A_{k}^{2}\left\lbrack {1 + \frac{1}{N_{ch}{SNR}}} \right\rbrack} + \left\langle {\mathbb{e}}^{2} \right\rangle}$

When the SNR and the channel count are sufficiently large that thebracketed terms can be neglected, these moments approach the coherentcase. Note that it is necessary for both the SNR and the channel countto be large compared to unity; when N_(ch)=1, quasi-coherent detectiondevolves to incoherent detection.

While Eq. 3 exhibits a bias in the estimate of A_(k), this bias shouldbe small in a system where the SNR is expected to be in excess of 40 dBand the number of channels around 32.

Coherent Detection using Disjoint Measurement Intervals

In the above, it is assumed that the available data was limited to onemeasurement interval, each measurement interval consisting of a largenumber of excitation intervals and observation intervals(sub-intervals). In practice, the system 100 will make measurementscontinually, and there will be a series of past measurements to exploit.

Referring to Eq. 1, disjoint measurement intervals are used for theestimates of A_(n) and Φ. Let the data from the prior measurementinterval be used to calculate {circumflex over (Φ)}, and let the datafrom the current measurement interval be used to calculate Â_(n). Thisdecorrelates the noise of the current measurement from the error in theestimate {circumflex over (Φ)}, and the resulting statistics aredifferent in the following way.

Because the noise components ε_(k) and δ_(k) are statisticallyindependent from cosψ and sinψ, the equations above can be simplified to$\begin{matrix}{{{E\left\{ {\hat{A}}_{k} \right\}} = {A_{k}E\left\{ {\cos\quad\psi} \right\}}}{E\left\{ {\hat{A}}_{k}^{2} \right\}} = {\frac{A_{k}^{2}}{2} + {\frac{A_{k}^{2}}{2}E\left\{ {\cos\quad 2\psi} \right\}} + {\frac{1}{2}E\left\{ {ɛ_{k}^{2} + \delta_{k}^{2}} \right\}}}} & {{Eq}.\quad 4}\end{matrix}$

These can be approximated${E\left\{ {\hat{A}}_{k} \right\}} \cong {A_{k} - \frac{A_{k}\left\langle {\mathbb{e}}^{2} \right\rangle}{2{\sum\limits_{n}A_{n}^{2}}}}$${E\left\{ {\hat{A}}_{k}^{2} \right\}} \cong {A_{k}^{2} - \frac{A_{k}^{2}\left\langle {\mathbb{e}}^{2} \right\rangle}{\sum\limits_{n}A_{n}^{2}} + \left\langle {\mathbb{e}}^{2} \right\rangle}$

At first blush, this appears to differ from Eq. 3 only superficially.However, the decorrelation of the errors means that this technique canbe modeled exactly as a coherent receiver with a small phase error inthe correlation kernel. The small phase error results in a scale factorerror, with expectation$\left\lbrack {1 - {\left\langle {\mathbb{e}}^{2} \right\rangle/\left( {2{\sum\limits_{n}A_{n}^{2}}} \right)}} \right\rbrack,$that is constant across all channels, so the results remainratiometrically accurate.

This technique relies on the stationarity of the phase shift betweenmeasurement intervals. However, performance is robust; for example, aphase error of 27° results in only a 1 dB scale factor error.

The Linear System Model

The relationship between a signal output by a marker 206 in response toan excitation from the excitation system 202 is modeled as follows.Assuming that marker saturation effects are neglected, a “markertransfer response” can be modeled as a second order bandpass function:${H_{b}(s)} = \left\lbrack \frac{RCs}{{L_{b}C_{s}^{2}} + {RCs} + 1} \right\rbrack$

with corresponding impulse response h_(b)(t).

The coupling between the current in the excitation source 202 and thevoltage sensed by a sensing coil 302 can be represented as a linearsystem shown in FIG. 10. As seen, an upper path through box 1001 is adirect feedthrough from source to sensor. A bottom path is the responseof the marker as seen by the sensing coil 302. The transfer function isthus:$\frac{V_{sense}(s)}{I_{exciation}(s)} = {{M_{se}s} - {\frac{M_{be}M_{sb}}{R}{s^{2}\left\lbrack \frac{RCs}{{L_{b}C_{s}^{2}} + {RCs} + 1} \right\rbrack}}}$

If the direct feedthrough path is ignored, a time domain block diagramof the linear system model is given by FIG. 11, where the filteringfunction is performed by convolution.

Analytic Signal Model

Assuming that bandpass signals are being processed, let:${\overset{\sim}{p}(t)} = {{{- j}\frac{A_{e}}{2}{\mathbb{e}}^{j\quad\omega_{e}t}{{rect}\left( {t/\tau_{e}} \right)}}\quad = {{- j}\sqrt{\frac{E_{e}}{2\tau_{e}}}{\mathbb{e}}^{j\quad\omega_{e}t}{{rect}\left( {t/\tau_{e}} \right)}}}$

be the analytic representation of the excitation pulse p(t) (i.e., thecurrent in the excitation source coil).

Hence$\quad{{p(t)} = {{2{Re}\left\{ {\overset{\sim}{p}(t)} \right\}}\text{}\quad = {A_{e}{\sin\left( {\omega_{e}t} \right)}{{rect}\left( {t/\tau_{e}} \right)}}}}$${\int{\mathbb{d}{{tp}^{2}(t)}}} = {{2{\int{{\mathbb{d}t}{{\overset{\sim}{p}(t)}}^{2}}}}\quad = E_{e}}$Here, A_(e) is the amplitude of the pulse, τ_(e) is its duration, andE_(e) is its energy. They are related according to E_(e)=A_(e) ²τ_(e)/2.Note that {tilde over (p)}(t) is not strictly analytic, except in thelimit of arbitrarily long pulse duration. As a consequence, theintegrals for the energy are not strictly equal unless τ_(e) is anintegral number of periods; we assume this is always the case and doesnot materially affect the conclusions herein.

We also approximate the analytic representation of the impulse responseof the resonant marker as{tilde over (h)} _(b)(t)=σ_(b) e ^(s) ^(b) ^(t)μ(t)

This is a single pole response that is accurate for a broad range offrequencies around the marker's resonant frequency, provided that Q issufficiently high, where$\zeta = {\frac{1}{2Q}\quad\text{damping~~~factor}}$−σ_(b)=−2πζf _(b) real part of the poleω_(b)=2π{square root}{square root over (1−ζ²)}f _(b) imaginary part ofthe poles_(b)=−σ_(b) +jω _(b) beacon's natural frequencyμ(t)=[1+sgn(t)]/2 unit step function

A Closed Form Expression for the Sensed Voltage from a Single Pulse

Using the analytic representations for the pulse and the marker impulseresponse, the analytic representation of the sensed voltage in FIG. 11can be obtained. To examine the effects of multiple markers andmarker/source mismatch, it is assumed that the excitation frequency isdifferent from the marker's resonant frequency (ω_(b)), i.e., ω_(e) isdistinct from ω_(b). It is helpful to define another natural frequencythat arises from the excitation.s_(Δ)=−σ_(b) +jω _(b) −jω _(e)

The receiver thus “sees” the following signal from the marker as [Eq.4]:${{\overset{\sim}{v}}_{sense}(t)} = {{{- \left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack}\frac{\mathbb{d}^{2}}{\mathbb{d}t^{2}}\left\{ {{\overset{\sim}{p}(t)}*{{\overset{\sim}{h}}_{b}(t)}} \right\}}\quad = {{{- \left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack}\frac{\mathbb{d}^{2}}{\mathbb{d}t^{2}}\left\{ {\int_{0}^{8}\quad{{\mathbb{d}x}{\overset{\sim}{p}\left( {t - x} \right)}{{\overset{\sim}{h}}_{b}(x)}}} \right\}}\quad = {{- {j\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack}}\frac{A_{e}}{2}\frac{s_{b}^{2}\sigma_{b}}{s_{\Delta}}{\mathbb{e}}^{s_{b}t}\left\{ \begin{matrix}{0\quad} & {{;{t < {{- \tau_{e}}/2}}}\quad} \\{{\left\lbrack {1 - \frac{s_{\Delta}}{s_{b}}} \right\rbrack^{2}{\mathbb{e}}^{{- s_{\Delta}}t}} - {\mathbb{e}}^{s_{\Delta}{\tau_{e}/2}}} & {;{{{- \tau_{e}}/2} \leq t \leq {\tau_{e}/2}}} \\{{{\mathbb{e}}^{{- s_{\Delta}}{\tau_{e}/2}} - {\mathbb{e}}^{s_{\Delta}{\tau_{e}/2}}}\quad} & {{;{{\tau_{e}/2} < t}}\quad}\end{matrix} \right.}}}$

There are three temporal regimes: prior to excitation, duringexcitation, and after excitation. In the third regime, the receivedsignal reverts to the marker natural frequency, weighted with a complexterm that is a function of the difference frequency between excitationand resonance.

FIG. 12 illustrates one example of a sensed response from a marker whenit is excited at resonance with a 12-cycle, 100 kHz pulse. It is thereal part of Eq. 4 with Q=40 and f_(b)=10⁵.

FIG. 13 shows the sensed response of a marker excited off-resonance. Thesame excitation pulse is used, but the marker is tuned to 88 kHz. Thedifference frequency is clearly visible, as is the marker's naturalfrequency decay. It is also clear that the excitation selectivity ispoor, as the response of the 88 kHz marker is suppressed only by afactor of about five.

Marker Saturation and Coherent Detection

Marker saturation is problematic, presenting both analytic and practicaldifficulties. Qualitatively, the effects of marker saturation on thesensed voltage will be as follows.

The peak of FIG. 12 will flatten out to a value relatively independentof the excitation amplitude.

During the excitation interval, the effective resonant frequency of themarker will increase, and the effective Q will decrease.

At the beginning of the observation interval (the third regime of Eq.4), the marker will relax out of saturation and decay in a linearfashion according to its natural frequency. However, we have to expectthat its initial conditions in this interval are, in practice,unknowable. In particular, the phase of the response in the observationinterval has to be treated as a random variable.

Give the above, it has been found that the signal in the observationinterval is relatively independent of the coupling term M_(be), thederivative operator associated with the induction between the source andmarker, and the duration of the excitation interval. Accordingly, amodel for the analytic sensed voltage in the observation interval can besimplified to:${{{\overset{\sim}{v}}_{sense}(t)} = {\left\lbrack \frac{M_{sb}}{R} \right\rbrack\frac{A_{sat}}{2}s_{b}{\mathbb{e}}^{s_{b}{({t - {\tau_{e}/2}})}}}};{{\tau_{e}/2} < t}$

where A_(sat) is a complex random variable.

The proper selection of τ_(e) (the duration of the excitation interval),{tilde over (k)}(t) (the complex correlation kernel), and the repetitioninterval of the excitation pulses is important for optimum performance.The selection may be made on an empirical basis and experimental datamay be used to determine these parameters.

Relative Sensitivity of a Coherent Detector: Single Pulse

There are sensitivity/selectivity trade-offs in the context ofsub-optimal correlation kernels. An optimum correlation kernel refers toa kernel which maximizes the SNR in a white noise environment. In anenvironment with multiple markers at different frequencies, there arebetter choices for kernels. The response of a receiver to a marker asthe system frequency changes is examined, i.e. predicting receiversensitivity as a function of frequency. Herein, the total measurementinterval is denoted as T₀.

There are three different cases examined:

Case 1: The linear system model applies. The receiver sensitivity overfrequency is referenced to a case in which the marker is excited with aconstant energy CW signal, at its resonant frequency, where the energyin the pulse is equal to the energy in the CW excitation. In this case,at marker resonance, the relative sensitivity equals the efficiency. Theuse of a constant energy comparison is meaningful when the energy in thepulse is limited by, for example, thermal or average exposureconsiderations.

Case 2: The linear system model applies. The receiver sensitivity overfrequency is referenced to a case in which the marker is excited with aconstant amplitude CW signal, at its resonant frequency, where theamplitude in the pulse is equal to the amplitude of the CW excitation.The use of a constant amplitude comparison is meaningful when the energyin the pulse is limited by, for example, source current or peak exposureconsiderations.

Case 3: All markers in the field are saturated. This is generally notrealistic when markers of different resonant frequencies are present,but the conclusions drawn are nonetheless instructive.

Case 1: Constant Energy

The CW Reference

The reference in this case assumes CW excitation exhibiting constantenergy E₀ over the measurement interval (same as the observationinterval), independent of its duration, at the marker's resonantfrequency. The sensed voltage is (using Eq. 4 in the second regime ofoperation, with τ_(e)→∞ and S_(Δ)→−σ_(b))${{\overset{\sim}{v}}_{sensereference}(t)} = {{{j\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack}{\sqrt{\frac{E_{0}}{2T_{0}}}\left\lbrack {1 + \frac{\sigma_{b}}{s_{b}}} \right\rbrack}^{2}s_{b}^{2}{\mathbb{e}}^{j\quad\omega_{b}t}}\quad \cong {{j\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack}\sqrt{\frac{E_{0}}{2T_{0}}}s_{b}^{2}{\mathbb{e}}^{j\quad\omega_{b}t}}}$

In the reference case, an optimal coherent receiver matched to themarker will exhibit a signal-to-noise ratio (see below analysis) of:${SNR}_{reference} \cong {{{\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack s_{b}^{2}}}^{2}\frac{E_{0}}{N_{0}}}$

Detector Characteristics over Frequency

Detection of the marker signal in the pulsed case is restricted to thethird regime of Eq. 4 to maintain (temporal) orthogonality with theexcitation signal. The observation interval is thus no larger thanT₀-τ_(e). The sensed voltage for t>τ_(e)/2 is:${{\overset{\sim}{v}}_{sense}(t)} = {\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack\sqrt{\frac{E_{e}}{2}}s_{b}^{2}\sigma_{b}{\hat{P}\left( s_{b} \right)}{\mathbb{e}}^{s_{b}t}}$

where {circumflex over (P)}(s) is a Laplace transform of {tilde over(p)}*(t), properly normalized (see further detail below).${\hat{P}\left( s_{b} \right)} = \frac{\int{{\mathbb{d}t}\quad{\mathbb{e}}^{s_{b}t}\overset{\sim}{p}*(t)}}{\left\lbrack {\int{{\mathbb{d}t}{{\overset{\sim}{p}(t)}}^{2}}} \right\rbrack^{1/2}}$

For an arbitrary kernel {tilde over (k)}(t), the signal-to-noise ratioof a coherent detector is $\begin{matrix}{{SNR}_{coherent} = {{{\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack s_{b}^{2}\sigma_{b}{\hat{P}\left( s_{b} \right)}}}^{2}\frac{{{\int{{\mathbb{d}t}\quad{\mathbb{e}}^{s_{b}t}{{\overset{\sim}{k}}^{*}(t)}}}}^{2}}{\int{{\mathbb{d}t}{{\overset{\sim}{k}(t)}}^{2}}}\frac{E_{e}}{N_{0}}}} \\{= {{{\left\lbrack \frac{M_{be}M_{sb}}{R} \right\rbrack s_{b}^{2}}}^{2}{{\sigma_{b}{\hat{P}\left( s_{b} \right)}{\hat{K}\left( s_{b} \right)}}}^{2}\frac{E_{e}}{N_{0}}}}\end{matrix}$

where the integration limits are understood to span the observationinterval. Setting E_(e)=E₀ for constant excitation energy, the relativesensitivity of a coherent correlation receiver, denoted ρ, is thus givenby [Eq. 5]: $\begin{matrix}{\rho = \frac{{SNR}_{coherent}}{{SNR}_{reference}}} \\{= {{\sigma_{b}{\hat{P}\left( s_{b} \right)}{\hat{K}\left( s_{b} \right)}}}^{2}}\end{matrix}$

This result facilitates computation and highlights the contribution ofthe correlation kernel in tailoring the selectivity of the receiver.

Example: Optimum Receiver for 100 kHz Marker, Q=40, 16 Cycle Pulse

The receiver observation interval is τ_(e)/2<t<∞, where τ_(e) is sixteencycles of the 100 kHz carrier. The normalized pulse and itscorresponding Laplace transform are thus${\overset{\_}{p}(t)} = {{- \frac{j}{\sqrt{\tau_{e}}}}{\mathbb{e}}^{{j\omega}_{e}t}{{rect}\left( {t/\tau_{e}} \right)}}$${\hat{P}\left( s_{b} \right)} = {\frac{j}{\sqrt{\tau_{e}}}\left\lbrack \frac{{\mathbb{e}}^{s_{\Delta}{\tau_{e}/2}} - {\mathbb{e}}^{{- s_{\Delta}}{\tau_{e}/2}}}{s_{\Delta}} \right\rbrack}$

The correlation kernel has a natural frequency:s _(r)=−σ_(r) +jω _(r)

where ω_(r)=ω_(e)=2π×10⁵ and σ_(r)=σ_(b). It is assumed that ^(σ) ^(b)is constant over all markers of interest. This implies that ω_(b)/Q isconstant.

The optimum kernel for a 400 kHz marker and its corresponding Laplacetransform are:{overscore (k)}(t)={square root}{square root over (2σ_(r) e ^(σ) ^(r)^(τ) ^(e) )}e ^(s) ^(r) ^(t)μ(t−τ _(e)/2)${\hat{K}\left( s_{b} \right)} = {- {\sqrt{2\sigma_{r}{\mathbb{e}}^{\sigma_{r}\tau_{e}}}\left\lbrack \frac{{\mathbb{e}}^{{({s_{\Delta} - \sigma_{r}})}{\tau_{e}/2}}}{s_{\Delta} - \sigma_{r}} \right\rbrack}}$

The relative sensitivity according to Eq. 5 is thus$\rho = {\frac{2\sigma_{b}^{2}\sigma_{r}}{\tau_{e}}{\frac{1 - {\mathbb{e}}^{s_{\Delta}\tau_{e}}}{s_{\Delta}\left( {s_{\Delta} - \sigma_{r}} \right)}}^{2}}$

The efficiency is determined by taking s_(Δ)→−σ_(b), whence$\eta = {\frac{1}{2\sigma_{b}\tau_{e}}\left\lbrack {1 - {\mathbb{e}}^{{- \sigma_{b}}\tau_{e}}} \right\rbrack}^{2}$

The efficiency is maximized for σ_(b)τ_(e)=2π/5, which justifies theselection of a 16 cycle pulse when Q is 40; in this case, the efficiencyis −6.9 dB. A plot of the relative sensitivity over 300 kHz to 5000 kHzis shown in FIG. 14. For comparison, the relative sensitivity of anincoherent receiver is also plotted.

Maximizing Efficiency in the Constant Energy Case

When the measurement interval T₀ is finite, the observation interval canbe denoted τ_(o)=T₀−τ_(e). For simplicity, as before, we assume no “deadzone” between the excitation and observation intervals. A one-cycle deadzone, which is expected in a practical system, will have a fraction of adB penalty. Using an optimum correlation kernel, the maximum availableefficiency becomes [Eq. 6]:$\eta = {{\frac{1}{2\sigma_{b}\tau_{e}}\left\lbrack {1 - {\mathbb{e}}^{{- \sigma_{b}}\tau_{e}}} \right\rbrack}^{2}\left\lbrack {1 - {\mathbb{e}}^{{- 2}\sigma_{b}\tau_{o}}} \right\rbrack}$

Efficiency can be used as a criterion when specifying excitation andobservation intervals in an operational system. As seen in FIG. 15, Eq.6 can be plotted as a function of the excitation and observationintervals, in carrier cycles normalized by the marker Q (usingσ_(b)=πf_(b)/Q).

In this case, efficiency is maximized for 0.4 Q excitation cycles, andan infinitely long observation interval (although 0.7 Q cycles ofobservation time is essentially optimum).

Case 2: Constant Amplitude

Setting E₀A₀ ²T₀/2 and E_(e)=A_(e) ²τ_(e)/2 in the SNR equations above,and setting A₀=A_(e) yields the relative sensitivity:$\rho_{{constant}\quad{amplitude}} = {\frac{\tau_{e}}{T_{0}}\rho}$

whence the maximum available efficiency in this case is$\eta_{{constant}\quad{amplitude}} = {{\frac{1}{2{\sigma_{b}\left( {\tau_{e} + \tau_{o}} \right)}}\left\lbrack {1 - {\mathbb{e}}^{{- \sigma_{b}}\tau_{e}}} \right\rbrack}^{2}\left\lbrack {1 - {\mathbb{e}}^{{- 2}\sigma_{b}\tau_{o}}} \right\rbrack}$

Efficiency in this case is shown in FIG. 16.

Case 3: Marker Saturation

Using the model of saturation developed above, it is straightforward toshow that, in this case: $\begin{matrix}{{SNR}_{reference} = {{{\left\lbrack \frac{M_{sb}}{R} \right\rbrack s_{b}}}^{2}\frac{{A_{sat}}^{2}T_{0}}{2N_{0}}}} \\{{SNR}_{coherent} = {{{\left\lbrack \frac{M_{sb}}{R} \right\rbrack s_{b}}}^{2}{{\hat{K}\left( s_{b} \right)}}^{2}\frac{{A_{sat}}^{2}}{2N_{0}}}}\end{matrix}$

The relative sensitivity is thus:$\rho_{saturation} = {\frac{{\mathbb{e}}^{\sigma_{b}\tau_{e}}}{T_{0}}{{\hat{K}\left( s_{b} \right)}}^{2}}$

Thus, if all markers are excited to saturation, the only frequencyselectivity is due to the correlation kernel. The maximum availableefficiency (when the optimum kernel is used) in this case is$\begin{matrix}{\eta_{saturation} = {\frac{1}{2{\sigma_{b}\left( {\tau_{e} + \tau_{o}} \right)}}\left\lbrack {1 - {\mathbb{e}}^{{- 2}\sigma_{b}\tau_{o}}} \right\rbrack}} & (8.1)\end{matrix}$

which is shown in FIG. 17. As seen, it is greatest for short excitationintervals, as the model used implicitly assumes the marker goes intosaturation immediately upon excitation.

Maximizing Efficiency: Periodic Pulses

Expressions for efficiency have been described for three differentcases, but each in the context of a single excitation pulse. Theseresults can be extended to the case of periodic excitation.

Consider N sequential measurement intervals, where the results of Nobservations are integrated prior to calculating the detected output andassuming that any residual marker response from earlier intervals can beneglected. In a white noise environment, the signal-to-noise will beproportional to N. However, the SNR for the CW reference cases used inthe efficiency calculations likewise scales as N, so the efficiencyremains constant. Hence FIGS. 15, 16, and 17 can be used for designguidance when specifying the measurement timing of the system. The firstcase, constant energy, probably best matches the operational constraintsof a practical system, whence the excitation interval should be in therange of 0.3-0.5 Q cycles and the observation interval about 0.6-1.0 Qcycles. Given the likelihood of marker saturation, the excitationinterval should be biased towards the low side.

On the Use of Windows for Frequency Selectivity

In the description above, the correlation kernels were chosen tomaximize the signal-to-noise ratio, and hence the efficiency. Withinthis framework, optimum choices for excitation and observation intervalswere developed for the single pulse and periodic pulse cases.

However, optimum kernels are optimum only in the sense of maximizing thesignal-to-noise ratio in a white noise environment. In an environmentconsisting of multiple markers, at multiple frequencies, use ofalternate kernels permits the tailoring of the selectivity of thereceiver. Indeed, in the extreme case of all markers being driven tosaturation, selectivity is a function of the kernel alone.

The nature of the relative sensitivity function (p) suggests the use ofwindows to control the frequency characteristics of the kernel. FIGS.18-20 show the effects of this. In all three cases, the excitation pulseis 16 cycles, and the marker Q is 40. It is assumed that the linearsystem model applies. The plots can be compared to FIG. 14 in which theoptimum kernel is used.

The first case (FIG. 18) uses a rectangular kernel of 32 cycles; it issimilar to the optimum case, but exhibits a slight loss of sensitivity(efficiency) at center frequency.

The second case (FIG. 19) uses a Hamming weighted kernel of 32 cycles;it exhibits somewhat more loss of sensitivity at center frequency, butthe selectivity is substantially improved.

The third case (FIG. 20) uses a Blackman weighted kernel of 32 cycles.The sensitivity is degraded by about 6.5 dB from the first case.

Locating the Marker Using Receiver Outputs

As noted above, in one embodiment, the sensing array has thirty-twosensing coils 302. After the receiver 208 has completed the signalprocessing detailed above, the resulting output of the receiver 208 isthirty-two “cleaned up” digital output signals. These digital outputsignals may then be used to locate the marker. As detailed in myco-pending U.S. patent application Ser. No. 10/679,801 filed Oct. 6,2003 entitled “Method and System for Marker Localization”, each digitaloutput signal is a measurement of one component of the magnetic fieldintegrated over the aperture of the sensor array. The location systemdetermines the location of the marker (i.e., marker location) from a setor array of measurements taken from the sensors (i.e., set of actualmeasurements). The location system compares the set of actualmeasurements to sets of reference measurements for various knownlocations within a bounding volume (also referred to as a localizationvolume). The bounding volume delimits the three-dimensional area inwhich the marker can be localized. A reference measurement for a knownlocation indicates the measurements to be expected from the sensors whenthe marker is located at that known location.

Based on the comparisons, the location system identifies the set ofreference measurements that most closely matches the set of actualmeasurements. The known location of the identified set of referencemeasurements represents the known location that is closest to the markerlocation, which is referred to as the “closest known location.” Thelocation system then uses sets of reference measurements for knownlocations near the closest known location to more accurately determinethe marker location when it is not actually at one of the knownlocations.

In one embodiment, the location system determines the marker locationbased on an interpolation of a set of calculated measurements from thesets of reference measurements of known locations near the closest knownlocation. Thus, the location system uses the set of referencemeasurements to find a known location that is close to the markerlocation to an accuracy that is dependent on the spacing of the knownlocations. The location system then uses an interpolation of sets ofreference measurements at known locations near the closest knownlocation to more accurately identify the marker location at a locationbetween the known locations.

Multiple Markers

In the description above, for simplicity and clarity, it is assumed thata single marker is being located or sensed. In some applications,multiple markers are associated with a subject or patient. In such acase, the teachings herein can easily be extended to multiple markers.For example, each marker may be excited at resonance individually in aserial fashion and located sequentially. Thus, the use of multiplemarkers is contemplated by the present claimed invention.

Conclusion

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense, that is to say, in the sense of“including, but not limited to.” Words using the singular or pluralnumber also include the plural or singular number, respectively.Additionally, the words “herein,” “above,” “below” and words of similarimport, when used in this application, shall refer to this applicationas a whole and not to any particular portions of this application. Whenthe claims use the word “or” in reference to a list of two or moreitems, that word covers all of the following interpretations of theword: any of the items in the list, all of the items in the list, andany combination of the items in the list.

The above detailed descriptions of embodiments of the invention are notintended to be exhaustive or to limit the invention to the precise formdisclosed above. While specific embodiments of, and examples for, theinvention are described above for illustrative purposes, variousequivalent modifications are possible within the scope of the invention,as those skilled in the relevant art will recognize. For example, anarray of hexagonally shaped sense coils may be formed on a planar arraycurved along at least one line to form a concave structure.Alternatively, the arrangement of coils on the panel may form patternsbesides the “cross” pattern shown in FIGS. 3A and 3B. The coils may bearranged on two or more panels or substrates, rather than the singlepanel described herein. The teachings of the invention provided hereincan be applied to other systems, not necessarily the system employingwireless, implantable resonating targets described in detail herein.These and other changes can be made to the invention in light of thedetailed description.

The elements and acts of the various embodiments described above can becombined to provide further embodiments. All of the above U.S. patentsand applications and other references are incorporated herein byreference. Aspects of the invention can be modified, if necessary, toemploy the systems, functions and concepts of the various referencesdescribed above to provide yet further embodiments of the invention.

These and other changes can be made to the invention in light of theabove detailed description. In general, the terms used in the followingclaims should not be construed to limit the invention to the specificembodiments disclosed in the specification, unless the above detaileddescription explicitly defines such terms. Accordingly, the actual scopeof the invention encompasses the disclosed embodiments and allequivalent ways of practicing or implementing the invention under theclaims.

One skilled in the art will appreciate that although specificembodiments of the location system have been described herein forpurposes of illustration, various modifications may be made withoutdeviating from the spirit and scope of the invention. Accordingly, theinvention is not limited except by the appended claims.

1. A system for locating a marker associated with a subject comprising:an excitation source for emitting an exciting waveform during anexcitation interval, said exciting waveform causing said marker toresonate; a sensing array including a plurality of sensing coils, saidsensing coils collectively outputting a plurality of inputs; and areceiver for analyzing said plurality of inputs to identify and correcta phase shift from said plurality of inputs to implement a coherentreceiver.
 2. The system of claim 1 wherein said receiver acts on saidplurality of inputs gathered during an observation interval.
 3. Thesystem of claim 2 wherein said receiver averages multiple sets of saidplurality of inputs over a plurality of said observation intervals priorto coherent analysis.
 4. The system of claim 1 wherein said excitingwaveform is a triangular waveform.
 5. The system of claim 1 wherein saidexcitation source and said sensing coil repeat the emission of saidexciting waveform and outputting of said plurality of receiver inputsfor a plurality of iterations, said receiver operative to averagemultiple sets of said plurality of receiver inputs over a plurality ofsaid observation intervals from said plurality of iterations prior tocoherent analysis.
 6. The system of claim 1 wherein said plurality ofinputs are acquired when said excitation source is inactive.
 7. Thesystem of claim 1 wherein said receiver includes a quadrature circuit.8. The system of claim 1 wherein said plurality of inputs are acquiredwhen a radiation source is inactive.
 9. The system of claim 5 whereinsaid exciting waveforms are randomly dithered.
 10. The system of claim 1wherein said phase shift is calculated based upon a least mean squareserror of said plurality of inputs.
 11. A method for locating a markerassociated with a subject comprising: providing an excitation source foremitting an exciting waveform during an excitation interval, saidexciting waveform causing said marker to resonate; providing a sensingarray including a plurality of sensing coils, said sensing coilscollectively outputting a plurality of inputs; and providing a receiverfor analyzing said plurality of inputs to identify and correct a phaseshift from said plurality of inputs to implement a coherent receiver.12. The method of claim 11 wherein said receiver acts on said pluralityof inputs gathered during an observation interval.
 13. The method ofclaim 12 wherein said receiver averages multiple sets of said pluralityof inputs over a plurality of said observation intervals prior tocoherent analysis.
 14. The method of claim 11 wherein said excitingwaveform is a triangular waveform.
 15. The method of claim 11 furtherincluding repeatiung the emission of said exciting waveform andoutputting of said plurality of receiver inputs for a plurality ofiterations, said receiver operative to average multiple sets of saidplurality of receiver inputs over a plurality of said observationintervals from said plurality of iterations prior to coherent analysis.16. The method of claim 11 wherein said plurality of inputs are acquiredwhen said excitation source is inactive.
 17. The method of claim 11wherein said receiver includes a quadrature circuit.
 18. The method ofclaim 11 wherein said plurality of inputs are acquired when a radiationsource is inactive.
 19. The method of claim 15 wherein said excitingwaveforms are randomly dithered.
 20. The method of claim 11 wherein saidphase shift is calculated based upon a least mean squares error of saidplurality of inputs.